An ML search for Lax connections recovers known spectral-parameter families in SU(2) PCM and S^2, but the low-loss candidate found for the non-symmetric coset T^{1,1} is a fake Lax connection, not a genuine integrability structure.
Complete integrability of geodesic motion in Sasaki-Einstein toric $Y^{p,q}$ spaces
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abstract
We construct explicitly the constants of motion for geodesics in the $5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. To carry out this task we use the knowledge of the complete set of Killing vectors and Killing-Yano tensors on these spaces. In spite of the fact that we generate a multitude of constants of motion, only five of them are functionally independent implying the complete integrability of geodesic flow on $Y^{p,q}$ spaces. In the particular case of the homogeneous Sasaki-Einstein manifold $T^{1,1}$ the integrals of motion have simpler forms and the relations between them are described in detail.
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Machine-Learning Search for Lax Connections
An ML search for Lax connections recovers known spectral-parameter families in SU(2) PCM and S^2, but the low-loss candidate found for the non-symmetric coset T^{1,1} is a fake Lax connection, not a genuine integrability structure.